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MIT OpenCourseWare · series 6 of 10

18.06 Linear Algebra

Gilbert Strang's course, the most-watched on the channel: elimination, the four subspaces, projections, determinants, eigenvalues and the SVD. Spring 2005.

36 lectures0 min

Episodes

  1. 1

    An Interview with Gilbert Strang on Teaching Linear AlgebraNot yet

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  2. Lec 1

    The Geometry of Linear EquationsNot yet

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  3. Lec 2

    Elimination with MatricesNot yet

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  4. Lec 3

    Multiplication and Inverse MatricesNot yet

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  5. Lec 4

    Factorization into A = LUNot yet

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  6. Lec 5

    Transposes, Permutations, Spaces R^nNot yet

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  7. Lec 6

    Column Space and NullspaceNot yet

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  8. Lec 7

    Solving Ax = 0: Pivot Variables, Special SolutionsNot yet

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  9. Lec 8

    Solving Ax = b: Row Reduced Form RNot yet

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  10. Lec 9

    Independence, Basis, and DimensionNot yet

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  11. Lec 10

    The Four Fundamental SubspacesNot yet

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  12. Lec 11

    Matrix Spaces; Rank 1; Small World GraphsNot yet

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  13. Lec 12

    Graphs, Networks, Incidence MatricesNot yet

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  14. Lec 13

    Quiz 1 ReviewNot yet

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  15. Lec 14

    Orthogonal Vectors and SubspacesNot yet

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  16. Lec 15

    Projections onto SubspacesNot yet

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  17. Lec 16

    Projection Matrices and Least SquaresNot yet

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  18. Lec 17

    Orthogonal Matrices and Gram-SchmidtNot yet

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  19. Lec 18

    Properties of DeterminantsNot yet

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  20. Lec 19

    Determinant Formulas and CofactorsNot yet

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  21. Lec 20

    Cramer's Rule, Inverse Matrix, and VolumeNot yet

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  22. Lec 21

    Eigenvalues and EigenvectorsNot yet

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  23. Lec 22

    Diagonalization and Powers of ANot yet

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  24. Lec 23

    Differential Equations and exp(At)Not yet

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  25. Lec 24

    Markov Matrices; Fourier SeriesNot yet

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  26. Lec 24b

    Quiz 2 ReviewNot yet

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  27. Lec 25

    Symmetric Matrices and Positive DefinitenessNot yet

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  28. Lec 26

    Complex Matrices; Fast Fourier TransformNot yet

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  29. Lec 27

    Positive Definite Matrices and MinimaNot yet

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  30. Lec 28

    Similar Matrices and Jordan FormNot yet

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  31. Lec 29

    Singular Value DecompositionNot yet

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  32. Lec 30

    Linear Transformations and Their MatricesNot yet

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  33. Lec 31

    Change of Basis; Image CompressionNot yet

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  34. Lec 32

    Quiz 3 ReviewNot yet

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  35. Lec 33

    Left and Right Inverses; PseudoinverseNot yet

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  36. Lec 34

    Final Course ReviewNot yet

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